V(PQ),V (PR), and V(PS) are 1. Find the volume of the parallelepiped PQRS if the vectors respectively 3î + 2ĵ – k, î – 2ĵ + 3k, and î – ĵ + k.

Q: Oil is leaking out of a ruptured tanker at the rate of r(t)=40e^(-0.03t) thousand liters per minute.…

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Q: B. Find the area of the region bounded by the following:

A: answer is in next step

Q: Fod ble Jecond deriyalive of Hhe Aullowing funchon g lx) = Inca=43)

A: g(x)=ln(x2+3)

Q: Determine whether each of the following functions is (a) continuous (b) differentiable 3. f(x) = v2…

A: If function 'f' is differentiable at x=c the f'(c) is the slope of the tangent of the function at…

Q: Find div F and curl F if F(x,y, z) = x°i – 5j + yzk. - div F= curl F=

A: A detailed solution is given below

Q: Let a be a real number and f(x, y) = 3ax?y + 6xy3. Let v = 3i – j and let V f(r, y) denote the…

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Q: Evaluate et-2 lim x→2 _x – 2 1 O +∞ O 1 O -00

A: Use l hospital rule for finding the correct option.

Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: Find div F and curl F if F(x, y, z) = 7e*" i - 10 cos yj+ 8 sin² z k. div F=| curl F=

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Q: Which type of discontinuity does the function exhibit at x = 3? %3D (-x2 + 1, -1 sx<0 2х, f(x) =…

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Q: Refer to the graph below. Find lim f(x). 3. 2- 1+ -5 4-3 -2 -1 -1+ 3. 4 5 x -2+ -3+ Does not exist 4…

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Q: A tank is being filled with a liquid. Z (1), given below, is the amount of liquid in liters in the…

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 1 n! n = 0…

A: By using the Direct Comparison Test to determine the convergence or divergence of the given…

Q: Evaluate F. dr. Jc F(x, y) = 7xi + 8yj C: r(t) = ti + v4 - tj, -2 st s 2

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Q: Evaluate the following limits. If needed, enter INF for oo and MINF for -oo. (a) lim (Va + 3r +1-1)=…

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Q: Use the figures to evaluate the function if f(x) = sin x. (x,1) f(a + B)

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Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: Evaluate lim,-(-- 7 - 10 + 4) | 4x3 O +∞ O -7 O -10 8.

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Q: Find curl(4= i+ 5x j+ 6y k). curl(4: i+ 5x j + 6y k) = ( i )i + ( i )j +( i

A: We have to find curl

Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. π 1 sin -x cos? 1

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal.…

A: Given that,      z=19xey-10ye-x

Q: Find curl (8z i + 9x j + 8y k). curl (8z i + 9x j + 8y k) = ( i )i + ( i )j + ( i )k

A: We know: Where P, Q and R correspond to the components of a given vector field:F→=Pi→+Qj→+Rk→ curl…

Q: Consider the following equations. f(x) = x5 + 3 %3D g(x) x + 3 %3D

A: The region is bounded by the graphs,  fx=x5+3 and gx=x+3

Q: A concert promoter needs to make $81,000 from the sale of 1800 tickets. The promoter charges $40 for…

A: x+y=1800x= number of $40 ticketsy= number of $70 tickets

Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

A: Given: r→t = 310t-sin10ti→+31-costj→ We know the following rt  =…

Q: Find the area of the surface generated by revolving the curve y = /2x – x2, from x = 0.25 to x =1.7

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Q: principle of mathematical induction

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Q: Consider the function f(x) = 4 – 7x² on the interval [- 5, 5]. Find the average or mean slope of the…

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Q: 2) Center: (11, 16) Radius: 1 4) Center: (-4, 0) Radius: 7 6) Center: (-7, -12) Radius: 3 8) Center:…

A: The Equation of a circle : (x - h)2 + (y - k)2 = r2 Where, r = Radius of the circle (h,k) = Center…

Q: Find the area of the region bounded by the given equations. Clearly state the integral(s) used to…

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Q: Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108…

A: In this question we have to find the minimum amount of tin sheet that can be made into a closed…

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: Determine the vector field of F. F(x, y) = yi – xj

A: Given that,  F(x,y)=yi-xj

Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

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Q: Consider the following. f(x) = x4 – 9x2 g(x) = x2 – 9 (a) Use a graphing utility to graph the region…

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Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: Find V· (F x G), if F(x, y, z) = 10xi +j+7yk and G(x, y, z) = xi+ yj – zk. V · (F × G) =

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Q: Find V x (V × F) if F(x, y, z) = 5xyj+ 10xyz k. V × (V × F) =

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Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: What is the radius of curvature at point (1, 2) of the curve 4x – y2 = 0.

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Q: 2x 1- cos x Graph f(x) = sin for Osxs2x by using transformations. 2 2- Use the graphing tool to…

A: To find: the graph of sin2x2 = 1-cosx2 for 0≤x≤2π Graph of cosx will be as following

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 30x from (30, 30) to (0, 0). %3D…

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Q: Vx² +y² and A metal plug has been designed using the intersection of the two cones z = x² + y2 += 1.…

A: We have to calculate volume of plug which is intersection of two cones z=√(x2+y2) and z/3+√(x2+y2)=1…

Q: Find the symmetric equations of the line that passes through the points (-2, 1, 0) and (1, 3, 5).

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Q: Find the exact length of the curve given by z = t° , y = t (0 <t< 4). Length

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Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

A: Given: x=2u4-u3+u-11, y=5u3-4u2-7u+2     As we know that; The Power rule; ddxxn=nxn-1 The Quotient…

Q: Determine whether the improper integral diverges or converges. 0. -4x xe dx converges O diverges…

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Q: a/a + b/b 189 a/b + b/a = 180 Find a and b value

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